Thermally induced evolution of pore geometry and its influence on hydrogen adsorption: A molecular dynamics approach

Thermally induced evolution of pore geometry and its influence on hydrogen adsorption: A molecular dynamics approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Thermally induced evolution of pore geometry and its influence on hydrogen adsorption: A molecular dynamics approach Utkir Uljayev, Shakhnozakhon Muminova, Erkin Vokhidov, Odiljon Sultonov This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8730613/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This article investigates the hydrogen storage capabilities of amorphous silicon dioxide ( a- SiO₂) and its structural characteristics that influence hydrogen adsorption. It emphasizes the advantages of a -SiO₂, such as its high surface area, low cost, and thermal stability, making it a promising candidate for large-scale hydrogen storage applications. The research employs molecular dynamics simulations to explore how temperature-dependent variations in pore size and structure affect hydrogen sorption efficiency. The findings reveal that slower cooling rates significantly increase pore size, enhancing hydrogen storage capacity, with optimal conditions yielding a maximum gravimetric density of 2.07 wt.% at 100 MPa. Despite its potential, the study notes that the hydrogen storage capacity of a -SiO₂ remains limited under standard room temperature conditions due to transformations of adsorbed hydrogen and structural limitations. The insights gained from this study are vital for future experimental research aimed at improving hydrogen storage in porous materials. Hydrogen storage silicon oxide molecular dynamics hydrogen physisorption hydrogen chemisorption Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 INTRODUCTION The ecological friendliness and sustainability of hydrogen energy have recently made it one of the most promising “green” fuels. It is considered a potentially efficient alternative fuel that can be used in several fields, including fuel cells [ 1 ], the electronics industry [ 2 ], and pharmaceuticals [ 3 ]. In hydrogen energy, the efficient storage of extracted hydrogen within materials is considered highly important [ 2 , 4 – 6 ]. Hydrogen is commonly stored in three main ways: as compressed gas [ 7 ], as cryogenic liquid [ 8 ], and in solid-state materials [ 9 ]. Nevertheless, in the compressed gas storage method, hydrogen occupies a significant volume [ 10 ]. In the cryogenic (liquid) storage method, additional energy is required to maintain the extremely low temperatures [ 11 ]. Furthermore, the low density of both compressed and liquid hydrogen, along with high costs associated with high-pressure storage and issues like boiling at room temperature, makes these storage methods unsuitable for large-scale applications [ 12 ]. The solid-state storage (SSS) method is considered relatively safer and more cost-effective compared to the other two methods. This approach is viewed as an efficient means of hydrogen storage, as it involves the absorption of hydrogen into nanomaterials [ 5 , 13 ]. Solid-state storage (SSS), hydrogen is stored in materials such as metal hydrides [ 9 ], complex hydrides [ 14 ], metal-organic frameworks (MOFs), covalent organic frameworks (COFs), carbon-based nanostructures [ 15 , 16 ] and porous materials, with the storage occurring via physisorption and chemisorption processes [ 17 , 18 ]. Recent research has increasingly focused on the use of porous materials as effective hydrogen storage mediums due to their high surface area and tunable properties, making them promising candidates for large-scale applications [ 15 , 16 , 18 , 19 ]. Specifically, materials composed of aluminum oxide (Al₂O₃) [ 19 – 21 ], titanium oxide (TiO₂) [ 22 – 24 ], zinc oxide (ZnO) [ 25 – 28 ], and silicon dioxide (SiO₂) [ 29 – 32 ] are considered effective for hydrogen storage due to their large surface areas and pore sizes [ 20 , 23 , 26 , 30 ]. These properties enhance the hydrogen storage capacity by providing more active sites for physisorption and chemisorption, thus improving the overall hydrogen storage performance. These materials have shown promising results in increasing hydrogen storage efficiency through their porous structures, making them suitable for advanced energy applications [ 20 , 23 , 26 , 30 ]. In particular, among these structures, SiO₂-based porous materials are being considered as potential candidates for hydrogen storage due to their harmlessness, low cost, and excellent thermal stability. These properties make SiO₂ an attractive option for hydrogen storage applications, as they provide a combination of safety, cost-effectiveness, and long-term durability, which are crucial factors for efficient energy storage systems. Moreover, their structural characteristics, including high surface area and porosity, further contribute to enhancing hydrogen adsorption, making them a viable material for large-scale energy storage solutions. Studies highlight the potential of SiO₂ in this context due to these advantageous properties [ 29 , 30 , 32 ]. SiO₂ structures are mainly found in two forms: crystalline ( c -SiO 2 ) [ 28 , 29 ] and amorphous amorf ( a -SiO 2 ) [ 33 , 34 ]. However, in recent years, a -SiO₂ structures have gained more attention for hydrogen storage applications due to their easier synthesis and practical advantages in this context [ 29 , 35 ]. Amorphous silica’s high surface area, porosity, and relatively simple preparation methods make it an attractive material for hydrogen storage systems. These properties, combined with its stability and cost-effectiveness, enhance its potential for use in large-scale energy storage solutions [ 29 , 35 ]. However, despite various experimental and theoretical studies on hydrogen storage through physisorption and chemisorption in a -SiO₂ structures [ 36 ], the hydrogen storage capacities of these structures remain quite low under normal conditions (room temperature and atmospheric pressure) [ 31 ]. Specifically, the transformation of hydrogen atoms/molecules adsorbed onto a -SiO₂ into other substances, depending on the pore volume, is considered one of the reasons for the low hydrogen storage capacity of these structuresa [ 37 ]. The positioning of pores in the structure (specifically, pockets, channels, tunnels, and voids) affects the adsorption of hydrogen. Therefore, in this study, the influence of pore structures on the adsorption process of hydrogen molecules in a -SiO 2 was investigated. MODELING METHOD AND DETAILS The mechanisms of hydrogen molecule (H 2 ) adsorption on amorphous silicon oxide ( a -SiO 2 ) were modeled through reactive molecular dynamics (MD) simulations, using the LAMMPS software package [ 38 ]. Initially, the a -SiO 2 structure model was created using the Chem3D software package (see Fig. 1 a). The generated structure consists of 3000 atoms, specifically 1000 silicon (Si) atoms and 2000 oxygen (O) atoms. In modeling the interactions between Si-O, O-O, and Si-Si pairs within the structure, the ReaxFF potential developed by Fogarty and colleagues was employed. This potential is based on the parameters established by Fogarty and his team to simulate reactive interactions in materials like a -SiO 2 [ 39 , 40 ]. The total system energy is the sum of several partial energy terms; these include energies related to lone pairs, undercoordination, overcoordination, valence and torsion angles, conjugation, hydrogen bonding, as well as van der Waals and Coulomb interactions [ 39 ]. In the isothermal-isobaric (NpT) ensemble, the a -SiO 2 structure was first heated to 2000 K at a rate of 1 K/ps over 1 ns using the Berendsen thermostat [ 41 ]. After this, the structure was cooled to 300 K at various cooling rates (i.e., 1, 5, 10, 50, 100, 500, 1000, 5000, 10000 K/ps). The heating and cooling process of the structures corresponds to the temperature rate (1 K/ps) used for the models of amorphous silicon, silicon, and silicon carbide, as referenced in the studies by tushadi [ 42 , 43 ]. Then, in the NVT ensemble, the system's temperature was controlled at 300 K for 100 ps using the Bussi thermostat [ 44 ] In simulations, the pressure of H 2 molecules in the system is calculated using the following expression [ 45 ]: $$\:p=J\sqrt{2\pi\:MRT}/{N}_{A}$$ 1 where J is the impingement flux (nm − 2 ⋅ns − 1 ), N A is Avagadro’s number, R is the universal gas constant, M is the molar mass of the H 2 molecule (kg⋅mol − 1 ) and T is the temperature of system (K). Specifically, in this simulation work, the pressures of H 2 molecules adsorbed onto the heated and cooled a -SiO 2 structures are 0.1, 1, 10, and 100 MPa. The incident particle (hydrogen molecule) is positioned at a z position of 10 Å above the uppermost Si or O atom of a -SiO 2 . The {x, y} coordinates of the incident particles are chosen randomly. Each impact is observed for 10 ps. The concentration of hydrogen molecules adsorbed on a -SiO 2 was calculated from the gravimetric capacity [ ]: $$\:wt.\%={\left({m}_{H}n/{({m}_{H}n+m}_{Si}N+{m}_{O}k\right))}^{1}\times\:100\%$$ 2 where \(\:{m}_{H}\) – mass of a hydrogen atom, \(\:{m}_{Si}\:\) – mass of a silicon atom in the system \(\:{m}_{O}\) - mass of the oxygen atom in the system, \(\:n\) – the number of hydrogen atoms adsorbed, \(\:N\:and\:k\) the number of silicon and oxygen atoms in the system, respectively. Each resulting value is obtained by averaging the results of 5 independent cases. The average density of thermally treated (i.e., heated and then cooled) a -SiO 2 structures is 2.26 g/cm³, which closely matches experimental (2.20 g/cm³ [ 46 , 47 ])and other simulation results (2.32–2.36 g/cm³ [ 48 ], 2.2 g/cm³ [ 49 ], 2.16–2.27 g/cm³ [ 50 ], 1.95–2.27 g/cm³ [ 51 ]) values, as shown in Fig. 1 a. Furthermore, the radial distribution function values for the distances between Si-O, O-O, and Si-Si atom pairs in the structure are 1.624 Å, 2.595 Å, and 3.173 Å, respectively. These values are very close to experimental (1.62 Å, 2.66 Å, and 3.12 Å) [ 52 ] and other simulation results (1.62 Å) [ 30 ], (1.61 Å, 2.51 Å, and 3.15 Å) [ 33 ], (1.6 Å, 2.5 Å, and 3.2 Å) [ 34 ], (1.654 Å, 2.63 Å, and 3.12 Å), as shown in Fig. 1 b. RESULTS AND THEIR ANALYSIS. 1. INTERACTION ENERGY The amount (number) of H 2 molecules adsorbed on a -SiO 2 was calculated based on the interaction energy. To determine the interaction distance (d cut ) at which physisorbed H 2 molecules interact with the a -SiO 2 surface, we use the average kinetic energy of the H 2 molecule and the interaction energy with a -SiO 2 , given by the energy point E = 5/2𝑘 𝐵 𝑇. The average binding distance (d cut ) of H 2 molecules with a -SiO 2 is 2 Å, and the average kinetic energy of H 2 molecules at 300 K is 0.065 eV. In our case, the interaction between a -SiO 2 and H 2 molecules corresponds to a range of 0–6 Å, which corresponds to an energy range of 0-0.08 eV, respectively (see Fig. 2 ) Therefore, in this study, the distance and energy between a -SiO 2 and H 2 molecules are selected within this range. The average physisorption distance of H 2 to amorphous SiO 2 typically ranges between 2.5 Å to 3.5 Å. This distance is characteristic of weak van der Waals interactions, as physisorption is generally governed by these forces rather than covalent bonding [ 53 ]. 2. CHANGES IN THE PORES OF THE STRUCTURE UNDER THE INFLUENCE OF TEMPERATURE. While the pore size in the a -SiO 2 structure was initially in the range of 2–4 Å (see Fig. 3 b), the pore size in a -SiO 2 heated and then cooled at different rates was in the range of 2 Å-4.5 Å. This change in pore size may later affect the hydrogen adsorption performance. In terms of quantity, nearly all structures had the highest number of pores in the range of 2.75 ± 0.7 Å. Additionally, as the cooling rate (K/ps) increased, the quantity of pores also increased. This indicates that the porosity level of the structure (both in terms of quantity and diameter) is increasing. During the analysis process, the quantity (number) and size (diameter) of the pores in the a -SiO 2 structure were analyzed (see Fig. 3 b). In Fig. 4 , as the cooling rate (K/ps) increased, the changes in the filled (V t ) and void (V b ) volumes in the structure were also analyzed. Specifically, as the cooling rate increases from 1 K/ps to 500 K/ps, the filled volume in the structure decreases linearly, while the void volume increases accordingly. Subsequently, with the increase in the cooling rate from 1000 to 10000 K/ps, the filled volume of the structure slightly increased, and then remained almost unchanged. This change indicates a significant change in structural properties with different cooling rates, which affects the density and porosity of the a -SiO 2 structure. The empty volume in the structure also exhibits a very small change accordingly. It can be concluded that the V t /V b , % ratio in the structure changes with the variation in the cooling rate. It should be noted that changes in these parameters, as mentioned above, can subsequently influence the hydrogen adsorption (storage) process. Observing the changes in the number of pores in the a -SiO 2 structure (see Fig. 3 b), the number of pores increases almost linearly with the rise in cooling rate. Initially, the increase in the number of pores is small (1–10 K/ps), but later, the increase becomes more significant (50–10,000 K/ps). 3. MECHANISMS OF HYDROGEN ADSORPTION The interaction between a -SiO 2 and H 2 molecules is crucial for understanding the hydrogen storage process in a -SiO 2 . The specific locations where H 2 molecules are adsorbed on the a -SiO 2 structure significantly influence the efficiency of both adsorption and absorption processes (see Fig. 5 ). Due to the amorphous nature of the thermolyzed structure, the adsorbed H 2 molecules interact differently with various regions of the surface see (Fig. 5 ). In this study, initially, 1000 H 2 molecules were adsorbed onto the a -SiO 2 structure at various coordinates, and their adsorption on the surface and absorption into the bulk were analyzed. As a result of the interaction between Si and O atoms in a-SiO₂ and hydrogen atoms, the formation of various silanol-related species was observed. Specifically, the presence of Si–OH groups (~ 0.01%) with an average bond length of approximately 0.98 Å (0.98 ± 0.04 Å from MD simulations, consistent with experimental values of 0.957 Å) was identified [ 54 ]. In addition, the formation of silane (Si–H, ~ 0.006%; see Fig. 5 c,d) and Si–O–H₂ configurations (see Fig. 5 a,b) was also detected [ 54 ]. Specifically, the oxygen (O) atoms on the surface and those near the surface with unbound electrons, along with dissociated hydrogen (H) atoms, interact to form silanol (Si − OH) bonds (~ 28.78%), and Si − H bonds at a distance of 1.64 Å [ 50 ]. This interaction is depicted in Fig. 5 d. These results are important for understanding the hydrogen adsorption and bonding behavior on the a -SiO 2 surface. As a result of the adsorption of H 2 molecules on the surface and inside the a -SiO 2 structure, the formation of Si-O-H 2 bonds (~ 71.22%) was observed. This included surface adsorption (~ 54.30%) and internal adsorption (~ 16.92%). Additionally, dissociated H atoms formed Si-O-H bonds (~ 28.78%), with surface adsorption (~ 23.14%) and internal adsorption (~ 5.64%). The bond lengths of Si-O-H and Si-O-H 2 ranged from 0.99–1.1 Å (MD) and 0.957 Å (experimental) [ 51 ]. In addition, a small amount of Si-H bonds (~ 0.015%) was observed, with weaker bonding (1.64 Å), and bond lengths in the range of 1.3–2.7 Å, as seen in both MD simulations and experimental data [ 51 ]. In general, the adsorbed H 2 molecules exhibit weak Van der Waals interactions, with approximately 22.56% of them located in the internal region and 77.44% near the surface (see Fig. 6 ). This suggests a preference for surface adsorption, with a smaller portion of the molecules interacting in the bulk phase, which could influence the overall hydrogen storage capacity and behavior within the a -SiO 2 structure. The distance at which H 2 molecules are adsorbed on the surface of a -SiO 2 is approximately 2 Å (see Fig. 2 ). Meanwhile, for H 2 molecules absorbed within the structure, the weak interaction distance with the a -SiO 2 framework is set between 2–3 Å [ 55 ]. At distances greater than this range, H 2 molecules prefer to position themselves between voids (empty spaces) within the a -SiO 2 structure [ 55 ], where their interaction with the material becomes negligible. This behavior of hydrogen molecules plays a critical role in the efficiency of hydrogen storage and its interaction with the material’s surface and internal voids. This aligns well with the calculations in previous studies, where similar trends in the adsorption and interaction behavior of H 2 molecules with a -SiO 2 have been observed [ 56 , 57 ]. The findings of weak interaction at greater distances and the preferential positioning of H 2 molecules in the voids further confirm the insights regarding the hydrogen storage mechanism in these materials. The change (decrease) in the number of adsorbed hydrogen atoms can be attributed to various factors. For instance, hydrogen atoms adsorbed on the surface of a -SiO 2 can desorb due to interactions with other hydrogen atoms, or from the dissociation of hydrogen atoms that were bound to surface oxygen or silicon atoms. These processes may cause hydrogen atoms to combine with other hydrogen atoms already present on the surface, leading to desorption [ 35 ].This desorption behavior is influenced by the specific arrangement of atoms and the dynamics of hydrogen interactions within the structure [ 35 ]. SiO 2 has a very stable structure where each silicon atom is bonded to four oxygen atoms, forming a three-dimensional network. This highly stable arrangement makes it difficult for hydrogen molecules to directly bond with the silicon or oxygen atoms. In other words, a -SiO 2 and H 2 do not form chemical bonds under normal conditions [ 58 ]. Therefore, in our case, most of the adsorbed H 2 molecules are bound to the surface near the surface area through physisorption. However, at high temperatures and pressures, or in the presence of catalysts, hydrogen can form chemical bonds with SiO 2 [ 58 ]. These conditions can activate reactions where hydrogen interacts with surface hydroxyl groups (Si-O-H) of a -SiO 2 , leading to the formation of silanol groups (Si-O-H). This may also result in other forms of hydrogenation on the silicon surface [ 50 ]. In such cases, the interaction between a -SiO 2 and hydrogen occurs through surface reactions, typically involving the dissociation of H 2 into H atoms. These hydrogen atoms then react with available surface sites, which can lead to an increase in the amount of adsorbed hydrogen. This process is often enhanced under conditions such as high temperatures, pressures, or in the presence of catalysts. If H 2 molecules adsorb onto defect-free regions of a -SiO 2 , they typically do so in the form of O 3 -Si-H and O 3 -Si-OH (as shown in Fig. 5 ) [ 50 ]. This adsorption process involves the interaction of hydrogen with the surface’s hydroxyl and silanol groups, forming stable chemical bonds that can alter the material’s properties, such as increasing its hydrogen storage capacity under certain conditions. 4. ANALYSIS OF HYDROGEN ADSORPTION UNDER PRESSURE As mentioned above (see Fig. 5 ), H 2 molecules adsorbed onto a -SiO 2 are adsorbed in various forms at different sites within the structure (see Fig. 7 a). After heating and cooling a -SiO 2 at different rates (K/ps), hydrogen molecules are adsorbed at various pressures (when placed in a hydrogen environment). The degree of hydrogen gravimetric density (wt.%) of these structures were analyzed (see Fig. 7 b). The results suggest that the cooling rate (K/ps) of the a -SiO 2 structure influences the hydrogen adsorption rate. Upon analyzing the changes in the size, diameter, and quantity of the pores in the structures cooled at different rates, it was observed that an increase in pore size correlates with a rise in hydrogen adsorption. This indicates that faster cooling rates may enhance the adsorption capacity due to the larger pore sizes, making it more favorable for hydrogen molecules to be trapped in the material. As observed in the results, the hydrogen storage performance at 10 MPa pressure did not increase linearly with the cooling rate (as shown in Fig. 7 b). Initially, with an increase in cooling rate from 1 K/ps to 5 K/ps, the hydrogen storage capacity improved, but after this point, the performance slightly decreased at 10 K/ps. As the cooling rate continued to increase (from 50 K/ps to 500 K/ps), there was a rise in the hydrogen storage capacity, followed by a sharp decline. This suggests that the hydrogen storage capacity did not consistently increase with the cooling rate. The highest storage capacity for 10 MPa pressure was observed at 500 K/ps. When comparing the hydrogen storage performance (coverage degree or wt.%) in a -SiO 2 structures cooled at rates ranging from 1 K/ps to 10000 K/ps, under different hydrogen pressures (0.1 MPa to 100 MPa), the following trends were observed: At 0.1 MPa pressure, the hydrogen storage capacity ranged from 0.13% to 0.14% or 0.01 wt% to 0.02 wt%, depending on the cooling rate. At 1 MPa, similar results were found with hydrogen storage increasing from 1.06% to 2.01% or 0.11 wt% to 0.13 wt%. At 10 MPa, the trend was consistent, ranging from 6.46% to 8.45% or 0.57 wt% to 0.92 wt%. At 100 MPa, the hydrogen storage increased from 17.16% to 21.12% or 1.69 wt% to 2.07 wt%. These findings indicate that the hydrogen storage capacity increases slightly with the cooling rate and pressure, but the overall increase is moderate across the studied pressures (see Fig. 8 a,b). It should be noted that heating amorphous silicon dioxide ( a -SiO 2 ) and cooling it at various rates can significantly affect its internal porous structure. The cooling rate particularly influences the quantity, shape, and volumetric size of the pores. During the cooling process, atoms within the amorphous material can rearrange, leading to the formation of new structures or altering the dimensions of existing ones. If amorphous silicon dioxide ( a -SiO 2 ) is cooled very quickly (> 0.1 K/ps), the pore size tends to be smaller, but their quantity might increase because the atoms do not have enough time to rearrange into a more ordered structure. This rapid cooling results in a higher internal stress and a denser internal structure. On the other hand, when the cooling process is slow (> 1000 K/ps), atoms have more time to adapt, leading to the formation of larger, more stable pores. In this case, the size of the pores increases, but their overall quantity might decrease. As a result, the material exhibits relatively low stress while maintaining a higher level of porosity. This phenomenon significantly impacts its mechanical properties and its ability to adsorb molecules, making it relevant for applications such as hydrogen storage. In general, at a temperature of 300 K and pressure ranges between 0.1 and 100 MPa, the maximum hydrogen adsorption coverage and gravimetric density on the surface of a -SiO 2 are 0.13% to 21.12% and 0.03 wt% to 2.07 wt%, respectively (see Fig. 8 ) The inability of H₂ molecules to enter the bulk of a -SiO₂ in correlation with the increasing size of the pores is due to the specific positioning and arrangement of the pores within the structure. Particularly, pores such as pockets, channels, tunnels, and voids (as shown in Fig. 9 ) prevent hydrogen molecules from penetrating the bulk [ 37 ]. Some of these voids are not accessible to hydrogen, which is influenced by the spatial characteristics and the nature of the pores themselves. As these voids are irregular or closed off, they block the hydrogen molecules from entering, even if the general porosity increases. The pore geometry plays a crucial role in determining the efficiency of hydrogen adsorption in such materials. The positioning of pores in the structure (pockets, channels and voids) affects the adsorption of hydrogen. The size and distribution of these pores influence how effectively hydrogen atoms or molecules can be stored on the material’s surface. Properly arranged pores can enhance the surface area available for hydrogen storage, thus improving adsorption capacity, while poorly structured pores may limit the interaction between hydrogen and the material, reducing its efficiency as a storage medium. Hydrogen molecules can enter specific types of pores in a -SiO 2 structures, such as Cleft/Groove, Invagination and Tunnel pores, but these pores are limited in size. However, the possibility of hydrogen molecules entering the channel pores is high. This is because in the channel pores, hydrogen atoms or molecules can move freely throughout the entire pore volume, which helps to trap hydrogen in the structure. In this study, the number and shape of pores in a -SiO 2 were changed using different cooling rates (K/ps), which in turn affected the amount of hydrogen adsorption. Understanding this behavior is very important for future experimental studies, especially for porous structures, as it will help to understand the adsorption of atoms and molecules in these systems. Conclusions Studying the hydrogen storage capabilities of amorphous silicon dioxide ( a -SiO 2 ) opens up valuable possibilities for structures with varying pore sizes. Although a -SiO 2 offers advantages such as high surface area, low cost, and cost-effectiveness, its potential for large-scale energy storage under standard room temperature conditions remains limited. This research investigates how temperature-dependent variations in the number and size of pores in a -SiO 2 structures influence hydrogen sorption, using molecular dynamics (MD) simulations. The study demonstrates that heating a -SiO 2 structures to specific temperatures causes changes in the number and diameter of the pores, depending on the cooling rate (K/ps). While slower cooling increases pore size significantly, faster cooling results in only a slight increase in pore size. This indicates that the cooling rate plays a crucial role in altering the pore structure of a -SiO 2 , which, in turn, affects the sorption of hydrogen atoms and molecules. The study also reveals that the maximum gravimetric density (coverage degree) of hydrogen at 10 MPa is achieved at a cooling rate of 500 K/ps, where it reaches 0.92 wt.% (8.45%). Overall, the maximum hydrogen gravimetric density (or coverage degree) at pressures from 100 MPa is 2.07 wt.% (or 21.12%). This study enhances the atomic-level understanding of the hydrogen adsorption mechanisms in various porous materials, with a particular focus on amorphous silicon oxide ( a -SiO 2 ). Declarations Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Contribution A.D., Sh.M., and U.U. were responsible for the conceptualization and preparation of the main manuscript, while E.V. and O.S. developed and finalized Figures 1-9. All authors critically reviewed and approved the final version of the manuscript. Acknowledgement This research was carried out within the framework of the F-FA-2021-512 project, granted by the Agency for Innovative Development of the Republic of Uzbekistan. The simulations were conducted using the computational resources available at the Institute of Ion-Plasma and Laser Technologies, Academy of Sciences of Uzbekistan. References S.K. Dash, S. Chakraborty, D. Elangovan, A Brief Review of Hydrogen Production Methods and Their Challenges. Energies. 16 , 1141 (2023) R. Krishna, E. Titus, M. Salimian, O. Okhay, S. Rajendran, A. Rajkumar, J.M.G. Sousa, A.L.C. Ferreira, J. Campos, J. Gracio, Hydrogen Storage for Energy Application, in Hydrogen Storage, edited by J. LiuInTech, (2012) J.A. Okolie, B.R. Patra, A. Mukherjee, S. Nanda, A.K. Dalai, J.A. Kozinski, Futuristic applications of hydrogen in energy, biorefining, aerospace, pharmaceuticals and metallurgy. Int. J. Hydrog Energy. 46 , 8885 (2021) K. Xia, Q. Gao, J. Jiang, H. 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Berendsen, J.P.M. Postma, W.F. Van Gunsteren, A. DiNola, J.R. Haak, Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81 , 3684 (1984) J. Sun, P. Liu, M. Wang, J. Liu, Molecular Dynamics Simulations of Melting Iron Nanoparticles with/without Defects Using a Reaxff Reactive Force Field. Sci. Rep. 10 , 3408 (2020) F.-J. Zhang, B.-H. Zhou, X. Liu, Y. Song, X. Zuo, Molecular dynamics simulation of atomic hydrogen diffusion in strained amorphous silica*. Chin. Phys. B 29 , 027101 (2020) G. Bussi, D. Donadio, M. Parrinello, Canonical sampling through velocity rescaling. J. Chem. Phys. 126 , 014101 (2007) U. Khalilov, A. Bogaerts, E.C. Neyts, Microscopic mechanisms of vertical graphene and carbon nanotube cap nucleation from hydrocarbon growth precursors. Nanoscale. 6 , 9206 (2014) K. Vollmayr, W. Kob, K. Binder, Cooling-rate effects in amorphous silica: A computer-simulation study. Phys. Rev. B 54 , 15808 (1996) J.R.G. Da Silva, D.G. Pinatti, C.E. Anderson, M.L. Rudee, A refinement of the structure of vitreous silica. Philos. Mag J. Theor. Exp. Appl. Phys. 31 , 713 (1975) A.J.H. McGaughey, M. Kaviany, Thermal conductivity decomposition and analysis using molecular dynamics simulations. Int. J. Heat. Mass. Transf. 47 , 1799 (2004) Z. Huang, Z. Tang, J. Yu, S. Bai, Thermal conductivity of amorphous and crystalline thin films by molecular dynamics simulation. Phys. B Condens. Matter. 404 , 1790 (2009) A.-M. El-Sayed, Y. Wimmer, W. Goes, T. Grasser, V.V. Afanas’ev, A.L. Shluger, Theoretical models of hydrogen-induced defects in amorphous silicon dioxide. Phys. Rev. B 92 , 014107 (2015) H. Fang et al., Ultrathin, transferred layers of thermally grown silicon dioxide as biofluid barriers for biointegrated flexible electronic systems, Proc. Natl. Acad. Sci. 113, 11682 (2016) R.L. Mozzi, B.E. Warren, The structure of vitreous silica. J. Appl. Crystallogr. 2 , 164 (1969) M. Bastos-Neto et al., Assessment of hydrogen storage by physisorption in porous materials. Energy Environ. Sci. 5 , 8294 (2012) S. Girard, J. Kuhnhenn, A. Gusarov, B. Brichard, M. Van Uffelen, Y. Ouerdane, A. Boukenter, C. Marcandella, Radiation Effects on Silica-Based Optical Fibers: Recent Advances and Future Challenges. IEEE Trans. Nucl. Sci. 60 , 2015 (2013) D.W. Use, Breck (Union Carbide Corporation, Tarrytown, New York) John Wiley and Sons, New York, London, Sydney, and Toronto. 1974. 771 pp. $ 11.95, J. Chromatogr. Sci. 13, 18A (1975) P.E. Blöchl, First-principles calculations of defects in oxygen-deficient silica exposed to hydrogen. Phys. Rev. B 62 , 6158 (2000) P.E. Bunson, M. Di Ventra, S.T. Pantelides, R.D. Schrimpf, K.F. Galloway, Ab initio calculations of H/sup +/ energetics in SiO/sub 2/: Implications for transport. IEEE Trans. Nucl. Sci. 46 , 1568 (1999) P.M. Carraro, F.A. Soria, E.G. Vaschetto, K. Sapag, M.I. Oliva, G.A. Eimer, Effect of nickel loading on hydrogen adsorption capacity of different mesoporous supports. Adsorption. 25 , 1409 (2019) Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8730613","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":599277456,"identity":"38a9b836-5faf-4c60-aba4-410d8219ad88","order_by":0,"name":"Utkir Uljayev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6ElEQVRIie3QsQrCMBCA4QuFuAS7VhR9hZZMYt/EJSLUpe4dRAJCXQRXH6clkKnvoCK4qrg4etUuDq0ZBfNDbroPkgDYbD8ZhQxnj0icVzxtAOeLeBNWErID8KgJKWPlcJgJ8ffpRCWgmLNWuhsmaklbK+XDIhzXEk2zvEBCNlHUjQvlUaanAnQ0l7WkJXNZEhlzPk+ReDHPiFQGZHu586EZwYu9yC4mJ1IR0UQ6OhK59GdIzsFxU8w6Kb7FFw1vaSvNbzIZ9YPt9JA9kpHr4o9510VYS6rrAQQfG6JxvWpgsmSz2Wz/2RN981VPudeWAAAAAABJRU5ErkJggg==","orcid":"","institution":"Arifov Institute of Ion-Plasma and Laser Technologies, Academy of Sciences of Uzbekistan","correspondingAuthor":true,"prefix":"","firstName":"Utkir","middleName":"","lastName":"Uljayev","suffix":""},{"id":599277457,"identity":"5b9c5e0f-1c48-4b37-b491-7ac8cefc98a2","order_by":1,"name":"Shakhnozakhon Muminova","email":"","orcid":"","institution":"Arifov Institute of Ion-Plasma and Laser Technologies, Academy of Sciences of Uzbekistan","correspondingAuthor":false,"prefix":"","firstName":"Shakhnozakhon","middleName":"","lastName":"Muminova","suffix":""},{"id":599277458,"identity":"c21de23c-6815-4d5b-b49f-b708de90c6e7","order_by":2,"name":"Erkin Vokhidov","email":"","orcid":"","institution":"National University of Uzbekistan named after Mirzo Ulugbek","correspondingAuthor":false,"prefix":"","firstName":"Erkin","middleName":"","lastName":"Vokhidov","suffix":""},{"id":599277459,"identity":"6b1ff661-0fc1-4431-91f4-b9cced834d1f","order_by":3,"name":"Odiljon Sultonov","email":"","orcid":"","institution":"University of economics and pedagogy","correspondingAuthor":false,"prefix":"","firstName":"Odiljon","middleName":"","lastName":"Sultonov","suffix":""}],"badges":[],"createdAt":"2026-01-29 11:08:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8730613/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8730613/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104781732,"identity":"a784446c-bd25-4657-afd5-540a5683b8fc","added_by":"auto","created_at":"2026-03-17 07:56:15","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":158321,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003ea\u003c/em\u003e) The \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2 \u003c/sub\u003estructure, with silicon (Si) and oxygen (O) atoms, is colored yellow and red, respectively. \u003cem\u003eb) \u003c/em\u003eRadial distribution function (RDF).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/a0964231a1affece3c9cd3ef.png"},{"id":104780894,"identity":"94041e0e-698a-4720-8769-deed1792f28f","added_by":"auto","created_at":"2026-03-17 07:54:13","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":8363,"visible":true,"origin":"","legend":"\u003cp\u003eAverage interaction energy H\u003csub\u003e2\u003c/sub\u003e molecule and \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/79d2ad138cb8bf5b69356b7a.png"},{"id":104781778,"identity":"da464728-9128-49af-8502-b87883bae1dd","added_by":"auto","created_at":"2026-03-17 07:56:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":585859,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003ea\u003c/em\u003e) Har xil tezlikda (K/ps) sovutilgan (300 K gacha) strukturalardagi g‘ovaklarning ko’rinishi, \u003cem\u003eb\u003c/em\u003e) Strukturadagi g’ovaklarlarning sovutish tezligiga bog‘liqligi.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/55424211d0b0a58c4ba968da.png"},{"id":104549795,"identity":"b8d42102-f83e-4245-b296-5b88cf24e83f","added_by":"auto","created_at":"2026-03-13 07:58:45","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":246071,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of the filled and empty volumes in the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2 \u003c/sub\u003estructure is presented.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/33006d7d57f3805ad3c8d9c5.png"},{"id":104781398,"identity":"f7d6bb6b-5df9-4fc8-80ca-680937170730","added_by":"auto","created_at":"2026-03-17 07:55:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":327606,"visible":true,"origin":"","legend":"\u003cp\u003eDespicts hydrogen atoms adsorbed on the surface and inside the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure. In the visualization, silicon (Si), oxygen (O), and hydrogen (H) atoms are represented\u003c/p\u003e\n\u003cp\u003eby yellow, red, and green colors, respectively.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/dee66b67aff68c40c20ec805.png"},{"id":104549802,"identity":"2cd5f4c9-baeb-479d-b967-53cd75bf67d6","added_by":"auto","created_at":"2026-03-13 07:58:45","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":96543,"visible":true,"origin":"","legend":"\u003cp\u003eSorption index of hydrogen molecules in \u003cem\u003ea-\u003c/em\u003eSiO\u003csub\u003e2\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/5fb7df8f5648ef3d14af9f54.png"},{"id":104781361,"identity":"1c9c8b32-2b59-4952-925c-fde28078f7d1","added_by":"auto","created_at":"2026-03-17 07:55:32","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":419207,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003ea\u003c/em\u003e) Hydrogens adsorbed on \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003eb\u003c/em\u003e) Dependence of hydrogen gravimetric density on cooling rate at different pressures.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/2d210f25f6d846abbc399342.png"},{"id":104780905,"identity":"25f7cea1-0cb4-43bc-8c96-71bb71b74d94","added_by":"auto","created_at":"2026-03-17 07:54:14","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":198581,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003ea\u003c/em\u003e) Dependence of the degree of hydrogen coverage on the cooling rate at different pressures, \u003cem\u003eb\u003c/em\u003e) Dependence of the gravimetric density of hydrogen on the cooling rate at different pressures.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/b024cc7d9d93690283ab4235.png"},{"id":104549799,"identity":"48f7b0c8-7e28-4af6-8703-bfd2c56ca9c2","added_by":"auto","created_at":"2026-03-13 07:58:45","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":340840,"visible":true,"origin":"","legend":"\u003cp\u003eTypes of pores \u0026nbsp;[37].\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/4b4af7099746b545fa8e4d1c.png"},{"id":107822760,"identity":"83934bf2-02e8-45f2-9263-c736ebefb732","added_by":"auto","created_at":"2026-04-26 11:09:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2760657,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8730613/v1/e527e32d-4799-4f2a-b17c-f766a1c53a96.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eThermally induced evolution of pore geometry and its influence on hydrogen adsorption: A molecular dynamics approach\u003c/p\u003e","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eThe ecological friendliness and sustainability of hydrogen energy have recently made it one of the most promising \u0026ldquo;green\u0026rdquo; fuels. It is considered a potentially efficient alternative fuel that can be used in several fields, including fuel cells [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], the electronics industry [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], and pharmaceuticals [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. In hydrogen energy, the efficient storage of extracted hydrogen within materials is considered highly important [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Hydrogen is commonly stored in three main ways: as compressed gas [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], as cryogenic liquid [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], and in solid-state materials [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eNevertheless, in the compressed gas storage method, hydrogen occupies a significant volume [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In the cryogenic (liquid) storage method, additional energy is required to maintain the extremely low temperatures [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Furthermore, the low density of both compressed and liquid hydrogen, along with high costs associated with high-pressure storage and issues like boiling at room temperature, makes these storage methods unsuitable for large-scale applications [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The solid-state storage (SSS) method is considered relatively safer and more cost-effective compared to the other two methods. This approach is viewed as an efficient means of hydrogen storage, as it involves the absorption of hydrogen into nanomaterials [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Solid-state storage (SSS), hydrogen is stored in materials such as metal hydrides [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], complex hydrides [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], metal-organic frameworks (MOFs), covalent organic frameworks (COFs), carbon-based nanostructures [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] and porous materials, with the storage occurring via physisorption and chemisorption processes [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Recent research has increasingly focused on the use of porous materials as effective hydrogen storage mediums due to their high surface area and tunable properties, making them promising candidates for large-scale applications [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSpecifically, materials composed of aluminum oxide (Al₂O₃) [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], titanium oxide (TiO₂) [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], zinc oxide (ZnO) [\u003cspan additionalcitationids=\"CR26 CR27\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], and silicon dioxide (SiO₂) [\u003cspan additionalcitationids=\"CR30 CR31\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] are considered effective for hydrogen storage due to their large surface areas and pore sizes [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. These properties enhance the hydrogen storage capacity by providing more active sites for physisorption and chemisorption, thus improving the overall hydrogen storage performance. These materials have shown promising results in increasing hydrogen storage efficiency through their porous structures, making them suitable for advanced energy applications [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn particular, among these structures, SiO₂-based porous materials are being considered as potential candidates for hydrogen storage due to their harmlessness, low cost, and excellent thermal stability. These properties make SiO₂ an attractive option for hydrogen storage applications, as they provide a combination of safety, cost-effectiveness, and long-term durability, which are crucial factors for efficient energy storage systems. Moreover, their structural characteristics, including high surface area and porosity, further contribute to enhancing hydrogen adsorption, making them a viable material for large-scale energy storage solutions. Studies highlight the potential of SiO₂ in this context due to these advantageous properties [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSiO₂ structures are mainly found in two forms: crystalline (\u003cem\u003ec\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e) [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] and amorphous amorf (\u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. However, in recent years, \u003cem\u003ea\u003c/em\u003e-SiO₂ structures have gained more attention for hydrogen storage applications due to their easier synthesis and practical advantages in this context [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Amorphous silica\u0026rsquo;s high surface area, porosity, and relatively simple preparation methods make it an attractive material for hydrogen storage systems. These properties, combined with its stability and cost-effectiveness, enhance its potential for use in large-scale energy storage solutions [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. However, despite various experimental and theoretical studies on hydrogen storage through physisorption and chemisorption in \u003cem\u003ea\u003c/em\u003e-SiO₂ structures [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], the hydrogen storage capacities of these structures remain quite low under normal conditions (room temperature and atmospheric pressure) [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSpecifically, the transformation of hydrogen atoms/molecules adsorbed onto \u003cem\u003ea\u003c/em\u003e-SiO₂ into other substances, depending on the pore volume, is considered one of the reasons for the low hydrogen storage capacity of these structuresa [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. The positioning of pores in the structure (specifically, pockets, channels, tunnels, and voids) affects the adsorption of hydrogen.\u003c/p\u003e \u003cp\u003eTherefore, in this study, the influence of pore structures on the adsorption process of hydrogen molecules in \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e was investigated.\u003c/p\u003e"},{"header":"MODELING METHOD AND DETAILS","content":"\u003cp\u003eThe mechanisms of hydrogen molecule (H\u003csub\u003e2\u003c/sub\u003e) adsorption on amorphous silicon oxide (\u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e) were modeled through reactive molecular dynamics (MD) simulations, using the LAMMPS software package [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. Initially, the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure model was created using the Chem3D software package (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea). The generated structure consists of 3000 atoms, specifically 1000 silicon (Si) atoms and 2000 oxygen (O) atoms. In modeling the interactions between Si-O, O-O, and Si-Si pairs within the structure, the ReaxFF potential developed by Fogarty and colleagues was employed. This potential is based on the parameters established by Fogarty and his team to simulate reactive interactions in materials like \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e]. The total system energy is the sum of several partial energy terms; these include energies related to lone pairs, undercoordination, overcoordination, valence and torsion angles, conjugation, hydrogen bonding, as well as van der Waals and Coulomb interactions [\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn the isothermal-isobaric (NpT) ensemble, the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure was first heated to 2000 K at a rate of 1 K/ps over 1 ns using the Berendsen thermostat [\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e]. After this, the structure was cooled to 300 K at various cooling rates (i.e., 1, 5, 10, 50, 100, 500, 1000, 5000, 10000 K/ps). The heating and cooling process of the structures corresponds to the temperature rate (1 K/ps) used for the models of amorphous silicon, silicon, and silicon carbide, as referenced in the studies by tushadi [\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e]. Then, in the NVT ensemble, the system's temperature was controlled at 300 K for 100 ps using the Bussi thermostat [\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eIn simulations, the pressure of H\u003csub\u003e2\u003c/sub\u003e molecules in the system is calculated using the following expression [\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e]:\u003c/p\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:p=J\\sqrt{2\\pi\\:MRT}/{N}_{A}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eJ\u003c/em\u003e is the impingement flux (nm\u003csup\u003e− 2\u003c/sup\u003e⋅ns\u003csup\u003e− 1\u003c/sup\u003e), N\u003csub\u003eA\u003c/sub\u003e is Avagadro’s number, \u003cem\u003eR\u003c/em\u003e is the universal gas constant, \u003cem\u003eM\u003c/em\u003e is the molar mass of the \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e molecule (kg⋅mol\u003csup\u003e− 1\u003c/sup\u003e) and T is the temperature of system (K).\u003c/p\u003e \u003cp\u003eSpecifically, in this simulation work, the pressures of H\u003csub\u003e2\u003c/sub\u003e molecules adsorbed onto the heated and cooled \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structures are 0.1, 1, 10, and 100 MPa.\u003c/p\u003e \u003cp\u003eThe incident particle (hydrogen molecule) is positioned at a z position of 10 Å above the uppermost Si or O atom of \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e. The {x, y} coordinates of the incident particles are chosen randomly. Each impact is observed for 10 ps.\u003c/p\u003e \u003cp\u003eThe concentration of hydrogen molecules adsorbed on \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e was calculated from the gravimetric capacity [ ]:\u003c/p\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:wt.\\%={\\left({m}_{H}n/{({m}_{H}n+m}_{Si}N+{m}_{O}k\\right))}^{1}\\times\\:100\\%$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{H}\\)\u003c/span\u003e\u003c/span\u003e – mass of a hydrogen atom, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{Si}\\:\\)\u003c/span\u003e\u003c/span\u003e– mass of a silicon atom in the system \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{m}_{O}\\)\u003c/span\u003e\u003c/span\u003e- mass of the oxygen atom in the system, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e – the number of hydrogen atoms adsorbed, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:N\\:and\\:k\\)\u003c/span\u003e\u003c/span\u003e the number of silicon and oxygen atoms in the system, respectively.\u003c/p\u003e \u003cp\u003eEach resulting value is obtained by averaging the results of 5 independent cases.\u003c/p\u003e \u003cp\u003eThe average density of thermally treated (i.e., heated and then cooled) \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003estructures is 2.26 g/cm³, which closely matches experimental (2.20 g/cm³ [\u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e])and other simulation results (2.32–2.36 g/cm³ [\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e], 2.2 g/cm³ [\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e], 2.16–2.27 g/cm³ [\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e], 1.95–2.27 g/cm³ [\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e]) values, as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea. Furthermore, the radial distribution function values for the distances between Si-O, O-O, and Si-Si atom pairs in the structure are 1.624 Å, 2.595 Å, and 3.173 Å, respectively. These values are very close to experimental (1.62 Å, 2.66 Å, and 3.12 Å) [\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e] and other simulation results (1.62 Å) [\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e], (1.61 Å, 2.51 Å, and 3.15 Å) [\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e], (1.6 Å, 2.5 Å, and 3.2 Å) [\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e], (1.654 Å, 2.63 Å, and 3.12 Å), as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb.\u003c/p\u003e"},{"header":"RESULTS AND THEIR ANALYSIS.","content":"\u003ch3\u003e1. INTERACTION ENERGY\u003c/h3\u003e\u003cp\u003eThe amount (number) of H\u003csub\u003e2\u003c/sub\u003e molecules adsorbed on \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e was calculated based on the interaction energy. To determine the interaction distance (d\u003csub\u003ecut\u003c/sub\u003e) at which physisorbed H\u003csub\u003e2\u003c/sub\u003e molecules interact with the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e surface, we use the average kinetic energy of the H\u003csub\u003e2\u003c/sub\u003e molecule and the interaction energy with \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e, given by the energy point E = 5/2𝑘\u003csub\u003e𝐵\u003c/sub\u003e𝑇. The average binding distance (d\u003csub\u003ecut\u003c/sub\u003e) of H\u003csub\u003e2\u003c/sub\u003e molecules with \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e is 2 Å, and the average kinetic energy of H\u003csub\u003e2\u003c/sub\u003e molecules at 300 K is 0.065 eV. In our case, the interaction between \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e molecules corresponds to a range of 0–6 Å, which corresponds to an energy range of 0-0.08 eV, respectively (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) Therefore, in this study, the distance and energy between \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e molecules are selected within this range.\u003c/p\u003e\u003cp\u003eThe average physisorption distance of H\u003csub\u003e2\u003c/sub\u003e to amorphous SiO\u003csub\u003e2\u003c/sub\u003e typically ranges between 2.5 Å to 3.5 Å. This distance is characteristic of weak van der Waals interactions, as physisorption is generally governed by these forces rather than covalent bonding [\u003cspan class=\"CitationRef\"\u003e53\u003c/span\u003e].\u003c/p\u003e\u003ch3\u003e2. CHANGES IN THE PORES OF THE STRUCTURE UNDER THE INFLUENCE OF TEMPERATURE.\u003c/h3\u003e\u003cp\u003eWhile the pore size in the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure was initially in the range of 2–4 Å (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb), the pore size in \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e heated and then cooled at different rates was in the range of 2 Å-4.5 Å. This change in pore size may later affect the hydrogen adsorption performance. In terms of quantity, nearly all structures had the highest number of pores in the range of 2.75 ± 0.7 Å. Additionally, as the cooling rate (K/ps) increased, the quantity of pores also increased. This indicates that the porosity level of the structure (both in terms of quantity and diameter) is increasing.\u003c/p\u003e\u003cp\u003eDuring the analysis process, the quantity (number) and size (diameter) of the pores in the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure were analyzed (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb). In Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, as the cooling rate (K/ps) increased, the changes in the filled (V\u003csub\u003et\u003c/sub\u003e) and void (V\u003csub\u003eb\u003c/sub\u003e) volumes in the structure were also analyzed. Specifically, as the cooling rate increases from 1 K/ps to 500 K/ps, the filled volume in the structure decreases linearly, while the void volume increases accordingly.\u003c/p\u003e\u003cp\u003eSubsequently, with the increase in the cooling rate from 1000 to 10000 K/ps, the filled volume of the structure slightly increased, and then remained almost unchanged. This change indicates a significant change in structural properties with different cooling rates, which affects the density and porosity of the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure. The empty volume in the structure also exhibits a very small change accordingly. It can be concluded that the V\u003csub\u003et\u003c/sub\u003e/V\u003csub\u003eb\u003c/sub\u003e, % ratio in the structure changes with the variation in the cooling rate. It should be noted that changes in these parameters, as mentioned above, can subsequently influence the hydrogen adsorption (storage) process. Observing the changes in the number of pores in the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb), the number of pores increases almost linearly with the rise in cooling rate. Initially, the increase in the number of pores is small (1–10 K/ps), but later, the increase becomes more significant (50–10,000 K/ps).\u003c/p\u003e\u003ch3\u003e3. MECHANISMS OF HYDROGEN ADSORPTION\u003c/h3\u003e\u003cp\u003eThe interaction between \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e molecules is crucial for understanding the hydrogen storage process in \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e. The specific locations where H\u003csub\u003e2\u003c/sub\u003e molecules are adsorbed on the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure significantly influence the efficiency of both adsorption and absorption processes (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDue to the amorphous nature of the thermolyzed structure, the adsorbed H\u003csub\u003e2\u003c/sub\u003e molecules interact differently with various regions of the surface see (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). In this study, initially, 1000 H\u003csub\u003e2\u003c/sub\u003e molecules were adsorbed onto the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure at various coordinates, and their adsorption on the surface and absorption into the bulk were analyzed. As a result of the interaction between Si and O atoms in a-SiO₂ and hydrogen atoms, the formation of various silanol-related species was observed. Specifically, the presence of Si–OH groups (~ 0.01%) with an average bond length of approximately 0.98 Å (0.98 ± 0.04 Å from MD simulations, consistent with experimental values of 0.957 Å) was identified [\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e]. In addition, the formation of silane (Si–H, ~ 0.006%; see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ec,d) and Si–O–H₂ configurations (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea,b) was also detected [\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e]. Specifically, the oxygen (O) atoms on the surface and those near the surface with unbound electrons, along with dissociated hydrogen (H) atoms, interact to form silanol (Si − OH) bonds (~ 28.78%), and Si − H bonds at a distance of 1.64 Å [\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e]. This interaction is depicted in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ed. These results are important for understanding the hydrogen adsorption and bonding behavior on the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e surface. As a result of the adsorption of H\u003csub\u003e2\u003c/sub\u003e molecules on the surface and inside the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure, the formation of Si-O-H\u003csub\u003e2\u003c/sub\u003e bonds (~ 71.22%) was observed. This included surface adsorption (~ 54.30%) and internal adsorption (~ 16.92%). Additionally, dissociated H atoms formed Si-O-H bonds (~ 28.78%), with surface adsorption (~ 23.14%) and internal adsorption (~ 5.64%). The bond lengths of Si-O-H and Si-O-H\u003csub\u003e2\u003c/sub\u003e ranged from 0.99–1.1 Å (MD) and 0.957 Å (experimental) [\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e]. In addition, a small amount of Si-H bonds (~ 0.015%) was observed, with weaker bonding (1.64 Å), and bond lengths in the range of 1.3–2.7 Å, as seen in both MD simulations and experimental data [\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e]. In general, the adsorbed H\u003csub\u003e2\u003c/sub\u003e molecules exhibit weak Van der Waals interactions, with approximately 22.56% of them located in the internal region and 77.44% near the surface (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThis suggests a preference for surface adsorption, with a smaller portion of the molecules interacting in the bulk phase, which could influence the overall hydrogen storage capacity and behavior within the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure. The distance at which H\u003csub\u003e2\u003c/sub\u003e molecules are adsorbed on the surface of \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e is approximately 2 Å (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). Meanwhile, for H\u003csub\u003e2\u003c/sub\u003e molecules absorbed within the structure, the weak interaction distance with the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e framework is set between 2–3 Å [\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e]. At distances greater than this range, H\u003csub\u003e2\u003c/sub\u003e molecules prefer to position themselves between voids (empty spaces) within the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure [\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e], where their interaction with the material becomes negligible. This behavior of hydrogen molecules plays a critical role in the efficiency of hydrogen storage and its interaction with the material’s surface and internal voids. This aligns well with the calculations in previous studies, where similar trends in the adsorption and interaction behavior of H\u003csub\u003e2\u003c/sub\u003e molecules with \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e have been observed [\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e]. The findings of weak interaction at greater distances and the preferential positioning of H\u003csub\u003e2\u003c/sub\u003e molecules in the voids further confirm the insights regarding the hydrogen storage mechanism in these materials.\u003c/p\u003e\u003cp\u003eThe change (decrease) in the number of adsorbed hydrogen atoms can be attributed to various factors. For instance, hydrogen atoms adsorbed on the surface of \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e can desorb due to interactions with other hydrogen atoms, or from the dissociation of hydrogen atoms that were bound to surface oxygen or silicon atoms. These processes may cause hydrogen atoms to combine with other hydrogen atoms already present on the surface, leading to desorption [\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e].This desorption behavior is influenced by the specific arrangement of atoms and the dynamics of hydrogen interactions within the structure [\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eSiO\u003csub\u003e2\u003c/sub\u003e has a very stable structure where each silicon atom is bonded to four oxygen atoms, forming a three-dimensional network. This highly stable arrangement makes it difficult for hydrogen molecules to directly bond with the silicon or oxygen atoms. In other words, \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003e do not form chemical bonds under normal conditions [\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e]. Therefore, in our case, most of the adsorbed H\u003csub\u003e2\u003c/sub\u003e molecules are bound to the surface near the surface area through physisorption. However, at high temperatures and pressures, or in the presence of catalysts, hydrogen can form chemical bonds with SiO\u003csub\u003e2\u003c/sub\u003e [\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e]. These conditions can activate reactions where hydrogen interacts with surface hydroxyl groups (Si-O-H) of \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e, leading to the formation of silanol groups (Si-O-H). This may also result in other forms of hydrogenation on the silicon surface [\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e]. In such cases, the interaction between \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e and hydrogen occurs through surface reactions, typically involving the dissociation of H\u003csub\u003e2\u003c/sub\u003e into H atoms. These hydrogen atoms then react with available surface sites, which can lead to an increase in the amount of adsorbed hydrogen. This process is often enhanced under conditions such as high temperatures, pressures, or in the presence of catalysts. If H\u003csub\u003e2\u003c/sub\u003e molecules adsorb onto defect-free regions of \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e, they typically do so in the form of O\u003csub\u003e3\u003c/sub\u003e-Si-H and O\u003csub\u003e3\u003c/sub\u003e-Si-OH (as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e) [\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e]. This adsorption process involves the interaction of hydrogen with the surface’s hydroxyl and silanol groups, forming stable chemical bonds that can alter the material’s properties, such as increasing its hydrogen storage capacity under certain conditions.\u003c/p\u003e\u003ch3\u003e4. ANALYSIS OF HYDROGEN ADSORPTION UNDER PRESSURE\u003c/h3\u003e\u003cp\u003eAs mentioned above (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e), H\u003csub\u003e2\u003c/sub\u003e molecules adsorbed onto \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e are adsorbed in various forms at different sites within the structure (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003ea). After heating and cooling \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e at different rates (K/ps), hydrogen molecules are adsorbed at various pressures (when placed in a hydrogen environment). The degree of hydrogen gravimetric density (wt.%) of these structures were analyzed (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003eb). The results suggest that the cooling rate (K/ps) of the \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structure influences the hydrogen adsorption rate. Upon analyzing the changes in the size, diameter, and quantity of the pores in the structures cooled at different rates, it was observed that an increase in pore size correlates with a rise in hydrogen adsorption. This indicates that faster cooling rates may enhance the adsorption capacity due to the larger pore sizes, making it more favorable for hydrogen molecules to be trapped in the material.\u003c/p\u003e\u003cp\u003eAs observed in the results, the hydrogen storage performance at 10 MPa pressure did not increase linearly with the cooling rate (as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003eb). Initially, with an increase in cooling rate from 1 K/ps to 5 K/ps, the hydrogen storage capacity improved, but after this point, the performance slightly decreased at 10 K/ps. As the cooling rate continued to increase (from 50 K/ps to 500 K/ps), there was a rise in the hydrogen storage capacity, followed by a sharp decline. This suggests that the hydrogen storage capacity did not consistently increase with the cooling rate. The highest storage capacity for 10 MPa pressure was observed at 500 K/ps.\u003c/p\u003e\u003cp\u003eWhen comparing the hydrogen storage performance (coverage degree or wt.%) in \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structures cooled at rates ranging from 1 K/ps to 10000 K/ps, under different hydrogen pressures (0.1 MPa to 100 MPa), the following trends were observed: At 0.1 MPa pressure, the hydrogen storage capacity ranged from 0.13% to 0.14% or 0.01 wt% to 0.02 wt%, depending on the cooling rate. At 1 MPa, similar results were found with hydrogen storage increasing from 1.06% to 2.01% or 0.11 wt% to 0.13 wt%. At 10 MPa, the trend was consistent, ranging from 6.46% to 8.45% or 0.57 wt% to 0.92 wt%. At 100 MPa, the hydrogen storage increased from 17.16% to 21.12% or 1.69 wt% to 2.07 wt%. These findings indicate that the hydrogen storage capacity increases slightly with the cooling rate and pressure, but the overall increase is moderate across the studied pressures (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003ea,b).\u003c/p\u003e\u003cp\u003eIt should be noted that heating amorphous silicon dioxide (\u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e) and cooling it at various rates can significantly affect its internal porous structure. The cooling rate particularly influences the quantity, shape, and volumetric size of the pores. During the cooling process, atoms within the amorphous material can rearrange, leading to the formation of new structures or altering the dimensions of existing ones. If amorphous silicon dioxide (\u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e) is cooled very quickly (\u0026gt; 0.1 K/ps), the pore size tends to be smaller, but their quantity might increase because the atoms do not have enough time to rearrange into a more ordered structure. This rapid cooling results in a higher internal stress and a denser internal structure. On the other hand, when the cooling process is slow (\u0026gt; 1000 K/ps), atoms have more time to adapt, leading to the formation of larger, more stable pores. In this case, the size of the pores increases, but their overall quantity might decrease. As a result, the material exhibits relatively low stress while maintaining a higher level of porosity. This phenomenon significantly impacts its mechanical properties and its ability to adsorb molecules, making it relevant for applications such as hydrogen storage.\u003c/p\u003e\u003cp\u003eIn general, at a temperature of 300 K and pressure ranges between 0.1 and 100 MPa, the maximum hydrogen adsorption coverage and gravimetric density on the surface of \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e are 0.13% to 21.12% and 0.03 wt% to 2.07 wt%, respectively (see Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e)\u003c/p\u003e\u003cp\u003eThe inability of H₂ molecules to enter the bulk of \u003cem\u003ea\u003c/em\u003e-SiO₂ in correlation with the increasing size of the pores is due to the specific positioning and arrangement of the pores within the structure. Particularly, pores such as pockets, channels, tunnels, and voids (as shown in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e) prevent hydrogen molecules from penetrating the bulk [\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e]. Some of these voids are not accessible to hydrogen, which is influenced by the spatial characteristics and the nature of the pores themselves. As these voids are irregular or closed off, they block the hydrogen molecules from entering, even if the general porosity increases. The pore geometry plays a crucial role in determining the efficiency of hydrogen adsorption in such materials.\u003c/p\u003e\u003cp\u003eThe positioning of pores in the structure (pockets, channels and voids) affects the adsorption of hydrogen. The size and distribution of these pores influence how effectively hydrogen atoms or molecules can be stored on the material’s surface. Properly arranged pores can enhance the surface area available for hydrogen storage, thus improving adsorption capacity, while poorly structured pores may limit the interaction between hydrogen and the material, reducing its efficiency as a storage medium.\u003c/p\u003e\u003cp\u003eHydrogen molecules can enter specific types of pores in \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structures, such as Cleft/Groove, Invagination and Tunnel pores, but these pores are limited in size. However, the possibility of hydrogen molecules entering the channel pores is high. This is because in the channel pores, hydrogen atoms or molecules can move freely throughout the entire pore volume, which helps to trap hydrogen in the structure. In this study, the number and shape of pores in \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e were changed using different cooling rates (K/ps), which in turn affected the amount of hydrogen adsorption. Understanding this behavior is very important for future experimental studies, especially for porous structures, as it will help to understand the adsorption of atoms and molecules in these systems.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eStudying the hydrogen storage capabilities of amorphous silicon dioxide (\u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e) opens up valuable possibilities for structures with varying pore sizes. Although \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e offers advantages such as high surface area, low cost, and cost-effectiveness, its potential for large-scale energy storage under standard room temperature conditions remains limited.\u003c/p\u003e \u003cp\u003eThis research investigates how temperature-dependent variations in the number and size of pores in \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structures influence hydrogen sorption, using molecular dynamics (MD) simulations. The study demonstrates that heating \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e structures to specific temperatures causes changes in the number and diameter of the pores, depending on the cooling rate (K/ps). While slower cooling increases pore size significantly, faster cooling results in only a slight increase in pore size. This indicates that the cooling rate plays a crucial role in altering the pore structure of \u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e, which, in turn, affects the sorption of hydrogen atoms and molecules. The study also reveals that the maximum gravimetric density (coverage degree) of hydrogen at 10 MPa is achieved at a cooling rate of 500 K/ps, where it reaches 0.92 wt.% (8.45%). Overall, the maximum hydrogen gravimetric density (or coverage degree) at pressures from 100 MPa is 2.07 wt.% (or 21.12%).\u003c/p\u003e \u003cp\u003eThis study enhances the atomic-level understanding of the hydrogen adsorption mechanisms in various porous materials, with a particular focus on amorphous silicon oxide (\u003cem\u003ea\u003c/em\u003e-SiO\u003csub\u003e2\u003c/sub\u003e).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of competing interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eA.D., Sh.M., and U.U. were responsible for the conceptualization and preparation of the main manuscript, while E.V. and O.S. developed and finalized Figures 1-9. All authors critically reviewed and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis research was carried out within the framework of the F-FA-2021-512 project, granted by the Agency for Innovative Development of the Republic of Uzbekistan. The simulations were conducted using the computational resources available at the Institute of Ion-Plasma and Laser Technologies, Academy of Sciences of Uzbekistan.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eS.K. Dash, S. Chakraborty, D. Elangovan, A Brief Review of Hydrogen Production Methods and Their Challenges. Energies. \u003cb\u003e16\u003c/b\u003e, 1141 (2023)\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR. Krishna, E. Titus, M. Salimian, O. Okhay, S. Rajendran, A. Rajkumar, J.M.G. Sousa, A.L.C. Ferreira, J. Campos, J. Gracio, Hydrogen Storage for Energy Application, in Hydrogen Storage, edited by J. 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Adsorption. \u003cb\u003e25\u003c/b\u003e, 1409 (2019)\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Hydrogen storage, silicon oxide, molecular dynamics, hydrogen physisorption, hydrogen chemisorption","lastPublishedDoi":"10.21203/rs.3.rs-8730613/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8730613/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis article investigates the hydrogen storage capabilities of amorphous silicon dioxide (\u003cem\u003ea-\u003c/em\u003eSiO₂) and its structural characteristics that influence hydrogen adsorption. It emphasizes the advantages of \u003cem\u003ea\u003c/em\u003e-SiO₂, such as its high surface area, low cost, and thermal stability, making it a promising candidate for large-scale hydrogen storage applications. The research employs molecular dynamics simulations to explore how temperature-dependent variations in pore size and structure affect hydrogen sorption efficiency. The findings reveal that slower cooling rates significantly increase pore size, enhancing hydrogen storage capacity, with optimal conditions yielding a maximum gravimetric density of 2.07 wt.% at 100 MPa. Despite its potential, the study notes that the hydrogen storage capacity of \u003cem\u003ea\u003c/em\u003e-SiO₂ remains limited under standard room temperature conditions due to transformations of adsorbed hydrogen and structural limitations. The insights gained from this study are vital for future experimental research aimed at improving hydrogen storage in porous materials.\u003c/p\u003e","manuscriptTitle":"Thermally induced evolution of pore geometry and its influence on hydrogen adsorption: A molecular dynamics approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-13 07:58:40","doi":"10.21203/rs.3.rs-8730613/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"91aee0dc-0072-4de8-8974-8bb9f714adcc","owner":[],"postedDate":"March 13th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-26T11:09:24+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-13 07:58:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8730613","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8730613","identity":"rs-8730613","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}